An electron is trapped in a box of length l = 100 pm. there is a single node in the center of the box where the electron cannot exist. what is the energy of the electron, in ev?

Answer is E= 24.092eV.

Explanation: This numerical is based on the Particle in 1-D box.

For a particle in 1-D box the energy is calculated by

where = allowed energies for a particle in a box

n = energy level

h = plank's constant

m = mass of a particle

L = length of a box

In this question, it is given the number of nodes from which we can calculate the value of "n"

Relationship between the number of nodes and the energy level is

l = number of angular nodes

Number of nodes given in the question is 1, so the energy level can be calculated from the above relation.

Now, putting all the values in energy formula,

Mass of electron =

n = 2

h =

Converting Joules to eV

okay yes , aha.